Question

Example of a combination:

A. Selecting a first-, second-, and third-place winner at a beauty competition
B. Picking 4 sets of towels out of 20 different sets
C. The number of ways 12 picture frames can be arranged in a row on a shelf
D. The number of ways 3 people can win 3 different prizes

Answer 1

Answer: B. Picking 4 sets of towels out of 20 different sets

In choice B, order does not matter.

Choices A, C, and D is when order does matter, which means they are examples of permutations.

Answer 2

A combination involves selecting items from a larger set without considering the order. Examples A and B provided are combinations, while examples C and D are permutations.

Step-by-step explanation:

Combination Examples

A combination is a way of selecting items from a larger set without regard to the order in which they are chosen. Let's go through the provided examples:

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• Example A: Selecting a first-, second-, and third-place winner at a beauty competition is an example of a combination. The order in which the winners are chosen does not matter.
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• Example B: Picking 4 sets of towels out of 20 different sets is also a combination. The specific order in which the sets are chosen does not affect the result.
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• Example C: The number of ways 12 picture frames can be arranged in a row on a shelf is an example of a permutation, not a combination. The order of arrangement matters in this case.
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• Example D: The number of ways 3 people can win 3 different prizes is a permutation, as the order in which the prizes are won matters.